CHAPTER IX

GEAR RATIOS; GEAR TRAINS; CHANGE GEARS

63. Gear Ratios.-The same principles as are applied to pulleys can be applied to gears. If we have two gears running together as shown in Fig. 17, the product of the diameter and r.p.m. of one gear will be equal to the product of the diameter and r.p.m. of the other. In studying gearing, we do not deal with the diameters so much as we do with the numbers of teeth. We find that gears are generally designated by the numbers of teeth. For

FIG. 17.-Pair of spur gears.

example, we talk of 16-tooth gears and 24-tooth gears, etc., but we seldom talk about gears of certain diameters.

In making these calculations for gears, we can use the numbers of teeth instead of the diameters. When a gear is revolving, the number of teeth that pass a certain point in one minute will be the product of the number of teeth times the r.p.m. of the gear.

If this gear is driving another one, as in Fig. 17, each tooth on the one gear will force one tooth along on the other one. Consequently, the product of the number of teeth times the r.p.m. of the second gear will be the same as for the first gear. This gives us our rule for the relation of the speeds and numbers of teeth of gears.

Rule for Finding the Speeds or Numbers of Teeth of Gears: Take the gear of which we know both the r.p.m. and the number of teeth and multiply these two numbers together. Divide their product by the number that is known about the other gear. The quotient will be the unknown number.

Example:

190 r.p.m.

A 38-tooth gear running 360 r.p.m. is to drive another gear at
What must be the number of teeth on the other gear?

38 X 360 = 13,680, the product of the number of teeth and revolutions
of one gear.

64. Gear and Pulley Trains.-A gear train consists of any number of gears used to transmit motion from one point to another. Figure 18 shows the simplest form of gear train, having but two gears. Figure 19 shows the same gears A and B, as in Fig. 18, but with a third gear, usually called an intermediate or idle gear, between them. The intermediate gear C can be used for either of two reasons:

96 T

FIG. 18.-Simple form of gear train.

1. To connect A and B and thus permit of a greater distance between the centers of A and B without increasing the size of the gears; or

2. To reverse the direction of rotation of either A or B. If A turns in a clockwise direction, as shown in both Figs. 18 and 19, B in Fig. 18 will turn in the opposite, or counterclockwise direction, but in Fig. 19, B will turn in the same direction as A.

The introduction of the intermediate gear C has no effect on the speed ratio of A to B. If A has 48 teeth and B 96 teeth, the speed ratio of A to B will be 2 to 1 in either Fig. 18 or Fig. 19. From Fig. 19 we can set up the proportion

In the case shown in Fig. 19, when A moves a distance of one tooth, the same amount of motion will be given to C, and C must at the same time move B one tooth. To move B 96 teeth, or one revolution, will require a motion of 96 teeth on A, or two revolutions of A. Hence, A will turn twice to each turn of B, or the speed ratio of A to B is 2 to 1, just as in the case of Fig. 18.

65. Compound Gear and Pulley Trains. Quite often it is desired to make such a great change in speed that it is practically necessary to use two or more pairs of gears or pulleys to accomplish it. If a great increase or reduction of speed is made by a single pair of gears or pulleys, it means that the difference in the diameters will have to be very great. The belt drive of a lathe is an example of a compound train of pulleys, though here the train is used chiefly for other reasons. In the first step the pulley on the line shaft drives a pulley on the countershaft; then another pulley on the countershaft drives the lathe. The back gearing on a lathe is an example of compound gearing, two pairs of gears being used to make the speed reduction from the cone pulley to the spindle and face plate.

Figure 20 shows a common arrangement of compound gearing. Here A drives B and causes a certain reduction of speed. B and C are fastened together and, therefore, travel at the same speed. A further reduction in speed is made by the two gears C and D. A and C are the driving gears of the two pairs and B and D are the driven gears.

The safest and surest method of calculating compound gear and pulley trains is to start with the gear or pulley of known diameter

and r.p.m.; work from that pulley or gear to the next; and thus proceed from one pulley or gear to another by the simple rules for the solution of pulleys and gears given in preceding paragraphs. Examples:

1. Let us calculate the speed ratio for the train of gears in Fig. 20. This would be the ratio of the r.p.m. of A to the r.p.m. of D.

Gear C is

Here we have used the same rule as we did for r.p.m. of B. the known gear, and its r.p.m. is .4N and its number of teeth is 16. We now find the ratio of the r.p.m. of A and D.

The N cancels out and leaves the ratio 10 to 1.

2. Let us take the pulley train of Fig. 21 and calculate the speed ratio of the pulleys A and D.